To study the effect it is convenient to resort to the vacuum emission picture [1]}, [2]}, providing an intuitive and straightforward framework for the study of photonic signatures of quantum vacuum nonlinearity in inhomogeneous electromagnetic fields.
In this approach [3]} the superposition of the driving electromagnetic fields gives rise to a signal-photon current, supplementing the outgoing fields with a signal-photon component constituting the signature of quantum vacuum nonlinearity.
In momentum space the latter can be expressed as
\(j_\nu (k)={\rm i}\int {\rm d}^4x\,{\rm e}^{-{\rm i}kx} \Bigl (k^\mu F_{\mu \nu }\frac{\partial {\cal L}_{\rm int}}{\partial {\cal F}}+ k^\mu {}^\star F_{\mu \nu }\frac{\partial {\cal L}_{\rm int}}{\partial {\cal G}}\Bigr )\,, \) 
